POLITECNICO DI MILANO · POLITECNICO DI MILANO ... developed in Adams/car prior to building the...

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POLITECNICO DI MILANO

School Of Industrial and Information Engineering

POLO REGIONALE DI LECCO

Master’s Thesis

Suspension Design Feasibility Study of Light Commercial Vehicle in ADAMS/Car

Supervisor: Prof. Francesco Braghin

Company supervisor : Mr. Vincenzo Abbatantuoni

Master Thesis by:

Sandip Kumar

Mat. No. 797008

October 2015

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DECLARATION

I hereby declare that this thesis, submitted to Politecnico di Milano as partial fulfillment of the requirements

for the degree of Master is completely novel and has never been presented at any other University for an

equivalent degree. I also certify that the document below has been exclusively done by me, with the

exception of certain standardized data and technique, the sources f o r wh i ch a r e appropriately cited in

the references. This thesis may be made available within the university library and may be photocopied

or loaned to other libraries for the purpose of consultation.

October 2015 Sandip Kumar

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ABSTRACT

In the present era of advancement in science and technology, computer aided engineering plays a pivotal role

in automotive industry. Now complete vehicle can be modeled and simulated for various road conditions.

Results have been obtained with high degree of accuracy for the same. There had been very good correlation

with the real time test data and simulated results. On some occasions simulation results had a better accuracy

while compared to the real test data. This boosted the confidence of industry and now, more and more tests

are performed with the help of CAE.

Following the same trend in this project a complete multibody model for a small passenger taxi car was

developed in Adams/car prior to building the real prototype. The modeling was done in accordance with the

dimensions obtained from CAD model. This ensured model was well with in design parameters. After

completion of the model, it was first evaluated at subsystem level extensively to see the design conformity

and eliminate any observed variation. Parallel and opposite wheel travel analysis was performed to simulate

bump, rebound and roll condition. After that full vehicle simulations were performed to assess straight line

stability, lane change performance and cornering behavior. All the results and outputs were discussed in

detail with the possibility of future application and works.

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ACKNOWLEDGEMENT

I take this opportunity to express my sincerest gratitude to my university supervisor Prof.

Francesco Braghin for his expert guidance and freedom of work he provided me throughout the project.

His constructive criticism and valuable suggestions motivated me to perform better than my capabilities.

I would also like to thank my company supervisor Mr. Vincenzo Abbatantuoni for giving me

this wonderful opportunity. His extensive support, patience and trust in my work kept me going in

difficult times and helped me in successful completion of the project. Along with this my gratitude goes

to Mr. Luca Marano for his expert comments and suggestions. His knowledge and understanding of

vehicle dynamics always inspired me to learn more.

A special thanks to Mr. Testi, Mr. Catelani and Mr. Brutti for their support and guidance with

Adams software. I would also like to extend my gratitude to Mr. Marchisio, Davide and Antonio for

helping me with performance parameters and design files.

I would like to thank my parents, jaji, my sisters Sarika, Nitu and my dear friend Ms. Rubina

Mahtab for their constant encouragement and support throughout this arduous journey, without which

this would not have been possible.

Last but not least a special mention to my extraordinary friends Dhanush, Shehzad, Arijit,

Bhuvan, Mukund, Shyam, Pradip, Ashish, Maddy, Geo, Vikas, Shahnawaaz, Amrita and Gesu who

never failed to boost my morale and encouraged me throughout this journey.

Thank you all.

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LIST OF FIGURES

Figure 1 Double wishbone suspension system ................................................................................................ 11

Figure 2 McPherson strut ................................................................................................................................. 12

Figure 3 Semi-trailing arm suspension ............................................................................................................. 13

Figure 4 Ackerman Geometry .......................................................................................................................... 14

Figure 5 Camber angle ..................................................................................................................................... 15

Figure 6 Toe angle ............................................................................................................................................ 15

Figure 7 Caster angle ....................................................................................................................................... 16

Figure 8 Kingpin and scrub radius .................................................................................................................... 16

Figure 9 Vehicle coordinate system in accordance with SAE convention ........................................................ 19

Figure 10 Rear suspension assembly ............................................................................................................... 21

Figure 11 Final assembly top view ................................................................................................................... 21

Figure 12 Final assembly front view ................................................................................................................ 22

Figure 13 Final assembly front ISO view .......................................................................................................... 22

Figure 14 Integration of MSC. ADAMS with CAE software .............................................................................. 24

Figure 15 Steps of suspension analysis ............................................................................................................ 25

Figure 16 MacPherson modelling component topology .................................................................................. 28

Figure 17 Front suspension links ...................................................................................................................... 29

Figure 18 Steering links .................................................................................................................................... 31

Figure 19 Front suspension assembly with test rig .......................................................................................... 32

Figure 20 Rear suspension assembly with test rig ........................................................................................... 34

Figure 21 Lumped mass body system .............................................................................................................. 35

Figure 22 Engine and powertrain system representation ................................................................................ 36

Figure 23 Front and rear tyres ......................................................................................................................... 37

Figure 24 Database for full vehicle assembly ................................................................................................... 37

Figure 25 Full vehicle assembly front view ...................................................................................................... 38

Figure 26 Full vehicle assembly side view ........................................................................................................ 38

Figure 27 Full vehicle assembly top view ......................................................................................................... 39

Figure 28 Full vehicle assembly Front-Iso ........................................................................................................ 39

Figure 29 Compliance matrix ........................................................................................................................... 40

Figure 30 Camber change Design of Experiment ............................................................................................. 42

Figure 31 Driving machine function ................................................................................................................. 48

Figure 32 Vehicle straight line test set-up ....................................................................................................... 49

Figure 33 Single and double lane change ........................................................................................................ 52

Figure 34 Add text ............................................................................................................................................ 55

Figure 35 Ramp steer test parameters ............................................................................................................ 55

Figure 36 Event builder .................................................................................................................................... 56

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LIST OF TABLES

Table 1 Specifications and target dimensions. ................................................................................................. 17

Table 2 Suspension parameters ........................................................................................................................ 19

Table 3 Type of joints and their respective degrees of freedom ........................................................................ 25

Table 4 Front parts and joints topology ............................................................................................................. 28

Table 5 Static parameter variable table ............................................................................................................ 28

Table 6 Steering system joints topology ........................................................................................................... 30

Table 7 Rear assembly joints topology ............................................................................................................. 33

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LIST OF GRAPHS

Graph 1 Power train map ................................................................................................................................. 35

Graph 2 Observed toe with sign change .......................................................................................................... 42

Graph 3 Toe adjustment geometry .................................................................................................................. 43

Graph 4 Modified toe with negligible sign change observed ........................................................................... 43

Graph 5 Caster and KPI v/s wheel travel curve ................................................................................................ 44

Graph 6 Front track change v/s wheel travel ................................................................................................... 44

Graph 7 Rear track change v/s wheel travel .................................................................................................... 45

Graph 8 Steer angle vs rack displacement ....................................................................................................... 46

Graph 9 Turn radius ......................................................................................................................................... 46

Graph 10 Ackerman error ................................................................................................................................ 47

Graph 11 Longitudinal vs lateral displacement ................................................................................................ 49

Graph 12 Front steering angle .......................................................................................................................... 50

Graph 13 Inclination angle vs time .................................................................................................................. 50

Graph 14 Lateral force vs time ........................................................................................................................ 51

Graph 15 Chassis displacement ....................................................................................................................... 53

Graph 16 Yaw rate and steering wheel angle at 50kmph ................................................................................ 53



Graph 19 Steering wheel angle v/s lateral acceleration .................................................................................. 57

Graph 20 Turning radius v/s steer wheel angle ............................................................................................... 57

Graph 21 Yaw rate v/s steer wheel angle ........................................................................................................ 58

Graph 22 Velocity v/s steer wheel angle ......................................................................................................... 58

Graph 23 Understeer curve ............................................................................................................................. 59

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TABLE OF CONTENT DECLARATION 2

ABSTRACT 3

ACKNOWLEDGEMENT 4

LIST OF FIGURES 5

LIST OF TABLES 6

LIST OF GRAPHS 7

1. INTRODUCTION 10

2. LITERATURE REVIEW 11

2.1 Introduction and Role of suspension system in a vehicle 11

2.2 Types of suspension system 11

2.2.1 Double wishbone suspension system: 11

2.2.2 McPherson strut suspension: 12

2.2.3 Semi-trailing arm rear axle: 13

2.3 Suspension system parameters 13

2.3.1 Ackerman 13

2.3.2 Camber 14

2.3.3 Toe 15

2.3.4 Caster 16

2.3.5 Kpi and scrub radius 16

2.3.6 17

3. DESIGN OF SUSPENSION COMPONENTS AND GEOMETRY 17

3.1 Choice of type of suspension system 17

3.1.1 Front suspension and steering system 18

3.1.2 Rear suspension system 18

3.2 Approach to CAD modeling and assembly of components. 18

3.3 Final representation of CAD model. 21

4. MODELING AND ANALYSIS IN ADAMS 23

4.1 Introduction to ADAMS/Car 23

4.2 Working principle 23

4.3 Approach to system modeling 26

4.3.1 Global reference coordinate 26

4.3.2 Local coordinate system 26

4.3.3 Markers 26

4.4 Approach to system modeling 26

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5. Conclusion 60

6. Appendix 61

4.4.1 Standard user interface 27

4.4.2 Template builder mode 27

4.4.3 System modeling 27

4.4.4 Modeling of front suspension assembly 27

4.4.5 Modeling rear suspension assembly 32

4.4.6 Body and chassis system 34

4.4.7 Powertrain assembly 35

4.4.8 Front and rear tyres modelling 36

4.4.9 Full vehicle assembly 37

4.5 Evaluation of suspension and steering characteristics 40

4.5.1 Definition of complex matrix 40

4.5.2 Wheel travel analysis 41

4.5.3 Steering analysis 45

4.6 Full vehicle simulation 47

4.6.1 Straight line maintain test 48

4.7 Single Iso-lane change maneuver 51

4.8 Ramp steer 55

6.1 Front assembly hardpoints. 61

6.2 Steering system 61

6.3 Rear suspension system 61

6.4 Body subsystem 62

6.5 Powertrain subsystem 62

6.6 Tire property file. 62

REFERENCES 68

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1. INTRODUCTION The company wanted to launch a new short wheel base passenger taxi car capable of seating 4 persons

including driver with a maximum payload of 450 Kgs. The vehicle was expected to be compact in size with

the sufficient ground clearance, affordable and durable enough for rough driving conditions. To make it

compact track width, wheel base and ground clearance was fixed according to the market survey and

benchmarked value.

So, the main goal was to develop a multibody model of the planned vehicle and analyze the suspension

behavior prior to build real prototype. This would show a broad picture of the real scenario and road

conditions. Any required modification or change in geometry, components would be possible to do at design

stage itself making project efficient in terms of time and money.

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2. LITERATURE REVIEW

2.1 Introduction and Role of suspension system in a vehicle The role of a car suspension is to maximize the friction between tires and the road surface to provide steering

stability with good handling and to ensure the comfort of the passenger. If the roads were perfectly flat then

there is no need of suspension system but unfortunately this is not the case. The role of suspension varies

between commercial and race cars. While the race car suspension system demands high performance without

any compromise to squeeze out minimum possible lap time, commercial vehicles require maximum life time

and durability of components with compromise in performance. The main aim of suspension system in

commercial vehicle is to have lowest amount of tire wear, minimum noise and vibration with maximum ride

comfort.

A good suspension system should provide best possible ride and handling performance, which is only

possible if wheel follows the road profile with very little tire fluctuation. The vehicle must be in steerable

condition at all times and driver should get a good response while maneuvering. This factor is ensured by the

fact that vehicle responds favorably to the forces generated by the tires during cornering or accelerating with

a good dive and roll geometry design

2.2 Types of suspension system In commercial or any other vehicle, chassis is the mainframe and must be able to handle the varying engine

power, acceleration, peak cornering speeds at all times which leads to the choice of independent suspension

system. Well known governing factors for this choice is low weight, no mutual wheel influence, little space

requirement, easier steerability, a kinematic or elasto-kinematic toe-in change and ease of adjustment. Low

weight and no mutual influence on the wheel are two important characteristics for good road handling on

uneven road surface with curves. Considering the above factors, independent suspension system was chosen.

While we speak of all the possible design and performance requirements there comes the engineer’s

nightmare to achieve all this within given constraints which is daunting. At various stages of design,

compromise had to be made to achieve a close to ideal performance. The design constraints have been

outlined by the problem statement for suspension system of small, lightweight, affordable and appealing

passenger car. The choice of suspension system and its components are guided mainly by required

investment, manufacturing cost, packaging constraints and performance benchmark values. All the design

constraints and bench marked values will be discussed and explained throughout the project.

2.2.1 Double wishbone suspension system:

Figure 1 Double wishbone suspension system

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It consists of two transverse links (control arms) on either side of the vehicle which are mounted to rotate on

the frame and connected on the outside to steering knuckle via ball joints. The greater the effective distance

between the transverse links, the smaller the forces in the suspension control arms and their mounting

becomes, i.e., the deformation in the component is smaller and wheel control is more precise.

Double wishbone suspension has great advantage with the kinematic possibilities. The inclination of control

arm can decide the height of body, roll and pitch while varying the length of the same influence the angle

movement of the compressing and rebounding wheels i.e. the camber and track width change.

With all the advantages in terms of vehicle performance and ease of adjustment this type of suspension

system is not suited for the vehicle under study. The main reason is requirement of larger control arms with

high inclination which is not possible with such a small track width and large cabin space requirement. It

would be extremely difficult to achieve a proper geometry with shorter arms and packaging space.

2.2.2 McPherson strut suspension:

Figure 2 McPherson strut

This type of suspension system is further development of double wishbone suspension. The upper control

arm is replaced by a pivot point on the wheel panel, which takes the end of the piston rod and the coil spring.

Forces from all the directions are concentrated at this point. The main advantage of the McPherson strut is

that all the suspension components can be combined into one assembly. The steering knuckle can be welded,

brazed or bolted firmly to the outer tube. Further advantages are lower forces in the chassis side of the

mounting, long spring travel and larger packaging space, as there is no upper control arm. Despite minor

disadvantages like lack of noise reduction and bulky structure, this type of suspension system fits right in

choice because of previously mentioned advantages and company’s experience in designing and

manufacturing this kind of suspension. Hence McPherson was chosen for front suspension of the vehicle.

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2.2.3 Semi-trailing arm rear axle:

Figure 3 Semi-trailing arm suspension

The semi-trailing arm rear suspension is characterized by balanced comfort and driving behavior. With the

semi-trailing arm rear suspension, the wheels are mounted on links that move at an angle to the vehicle’s

longitudinal axis as they deflect and rebound. The compact design also allows for a large luggage

compartment. When wheel goes in bump and rebound-travel they cause spatial movement, so the drive shafts

need two joints per side with angular mobility and length compensation. The horizontal and vertical angles

determine the roll steer properties. Camber and toe-in changes increase, the bigger the angles are. Semi-

trailing axles have an elasto-kinematic tendency to oversteer. With the ease of driveshaft mounting and

available wheel travel it was selected for rear suspension system.

2.3 Suspension system parameters

The kinematics of the suspension system can be visualized as a body moving in space relative to another

body with three components of translation and three components of rotation. While the independent type

suspension system allows for relative motion between the wheel and the vehicle body without affecting the

other wheel, it has only one path of motion. Like any other single body, wheel has six degrees of freedom in

space out of which five dof’s are restrained by the suspension linkages. These linkages also severely limit the

orientation of the wheel as it travels in jounce and rebound against spring and damper which can rotate about

its three axes due to the geometry of the suspension. These rotation deviate the geometry from the ideal

suspension design. At maximum, the designer can try to offset the effect of such rotations with fine tuning

the geometry but still it would result in change in camber, caster and toe-angle. An insight to the same has

been briefly discussed below.

2.3.1 Ackerman When front wheel drive vehicle is steered away from straight-ahead position, the design of steering linkage

determines whether the wheels stay parallel or one wheel steers more than the other. This difference in steer

wheel angle is the effect of Ackerman geometry and the device which provides this effect is called

Ackerman steering. There is no four bar linkage mechanism which can give a perfect Ackerman geometry,

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but a close to perfect condition could be achieved. The condition to meet this criterion is that vehicle must be

driving slowly and free from any lateral forces. Since the passenger cars are designed for low lateral

acceleration use, it is preferred to use Ackerman geometry.

The Ackerman condition is expressed by the following formula:

Where: is the steer angle of outer wheel

is the steer angle of inner wheel

w is the trackwidth

l is the wheelbase

Figure 4 Ackerman Geometry

2.3.2 Camber Camber angle is the angle that the wheel plane makes with the vertical axis. It is positive when the top of the

wheel leans outwards, away from the vehicle body and negative when it is inwards. Cornering force of the

tyre depends on its angle relative to the road surface. Hence camber is a major contributing factor for good

road grip. When the tyre moves on the road the rubber is elastically deformed, as the tread is pulled through

the tyre/road interface, which causes an additional lateral force known as camber thrust. Due to the

contribution of this camber thrust, tyre develops its maximum lateral force at a small camber angle. Hence it

is suggested to provide a small amount of camber angle in the direction of wheel rotation to optimize tyre

performance during the turn.

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Figure 5 Camber angle

Passenger cars are designed with soft roll stiffness to provide a smooth ride. This low roll stiffness results in

large wheel travel causing large camber change and eventually reduced tyre performance and excessive

wear. Therefore, within the given parameters a compromise must be made to achieve a balance between the

two, which has been discussed during suspension analysis.

2.3.3 Toe It is the angel between the longitudinal axis of the vehicle and the line of intersection of the wheel plane and

the vehicle XY plane. It is positive if the wheel front is rotated towards the vehicle body and vice versa.

Figure 6 Toe angle

It can be expressed in degrees or radians but it is more common to express it as the difference between the

track width measured at leading and trailing edges of the tyre. Toe control is important as it directly affects

three major performances, i.e. corner entry handling, straight line stability and tyre wear. When a car is

running in a straight line, the wheels in the given axle should directly point ahead, for maximum power and

low tyre wear. Directional stability of the vehicle is increased by toe-in, while toe-out increases the steering

response. Too much of toe-in causes rapid wear at the outer edges of the tyre and vice versa.

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2.3.4 Caster

Caster angle is the angle in the side elevation (vehicle XZ plane) between the steering (kingpin) axis and the

vehicle axis. It is positive when the top of the steer axis is inclined rearwards and vice versa.

Figure 7 Caster angle

A negative caster helps in quick steer return, increases the straight-line ability of the vehicle, provides a large

tyre contact patch area during turn and good steering feel. But if the caster is increased to a large value it will

also cause an undesired increase in steering effort.

2.3.5 Kpi and scrub radius The Kingpin inclination (KPI) or steering axis inclination (SAI), is the angle formed between vertical and the

line joining the upper and lower ball joints (steering axis). It affects the self retuning mechanism of the

steering to straight ahead position, bringing the wheel to its highest point. Positive kingpin is defined with

the upper ball joint closer to the chassis than the lower. Kingpin is also used to set scrub radius, which can be

adjusted to zero value when the steering axis coincides with the tyre centerline on the ground. But excessive

KPI and high steering angles lead to positive camber change and corner weight variations.

Figure 8 Kingpin and scrub radius

Scrub radius, also known as kingpin offset, is the lateral distance between the centerline of the wheel and

intersection of the kingpin axis at the ground. A large scrub radius means reduced steering effort at the cost

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of increased friction which causes the tyre to scrape through the surface while turning, as the tyre no more

turns along the center line. So it is desirable to minimize the scrub radius in order to make the

steering less sensitive to road irregularities, braking etc. A zero scrub radius eliminates the negative effects

on the steering but will also leave the driver with a dead feel of the steering. of Acceptable scrub radius

is thought to be those smaller than 25% of the tread width.

3. DESIGN OF SUSPENSION COMPONENTS AND GEOMETRY

Before proceeding to the design of suspension components and related geometry, a comprehensive market

survey was done by the company to find out the customer requirements and market needs. Then based on the

inputs from the survey benchmarking process was carried out. The basic requirement of the vehicle was it

should be low cost, light weight, spacious and full fill the needs of south east Asian countries.

Proceeding with this idea, first size and general specification of the vehicle was decided as follows.

Length ≤ 3 m

Width ≤1.5 m

Height 2.5 m

Ground clearance 0.240 m

Kerb weight ≤450 KG

Wheel radius 12 inches

Engine 230cc water cooled

Transmission Manual, Rear wheel drive

Table 1 Specifications and target dimensions.

Next a decision had to be made for the track width and wheel base of the vehicle. For this one constraint was

already defined as length and width of the vehicle. Second was influenced by the fact that interior of the

vehicle must be spacious along with the provision of luggage compartment. So a wheel base of 1.8m and

track width of 1.2 m was proposed. Keeping in mind the road irregularities a target ground clearance of

0.240 m was also decided. These three values were subject to minor changes as the design would progress.

3.1 Choice of type of suspension system

During this process a comparative study on various types of suspension system for front and rear was done.

Reasoning for the same has been discussed in the following section.

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3.1.1 Front suspension and steering system As the wheel base was fixed and it had been stated that interior should spacious then it became quite obvious

that front driver and passenger seats would be located close to the wheel envelop. Considering these facts,

there were two good possible choices. It was either double wishbone suspension or McPherson strut type

suspension system.

Double wishbone suspension required two transverse links (control arms) on either side of the vehicle which

would be mounted to rotate on the frame and connected on the outside to steering knuckle via ball joints.

This kind of suspension provided good control over geometry and improved behavior in dynamic condition.

But major disadvantage came in terms of packaging issue. Placement of upper arm required a large wheel

envelop and that would cramp the driver and front passenger leg space. It also required more components

(upper A-arm, extra bushings and ball joints for mountings) and assembling time. In terms of ergonomics

and cost it was not a perfect choice. This ruled out any scope of using double wishbone type suspension.

Second best choice for front was McPherson strut type suspension system. This is a further development of

double wishbone suspension as top. A-arm is replaced by the strut system. It only required lower control arm

mounting and placement of strut in vehicle body full filing the criteria of large cabin space. It also needed

less number of components and assembling time, so in terms of cost also it was an advantage to use this. The

final factor which dominated this choice was company’s previous experience in this type of suspension and

readily available assembly components and no need for any new investment. Hence for front, McPherson

strut suspension was decided.

For steering system rack and pinion type steering system was selected keeping in mind its simple and

effective design. This type of steering also provided a good possibility of having good Ackerman geometry.

Assembly and mounting would also take less space.

3.1.2 Rear suspension system During the market survey and benchmarking process choice of engine was also locked. Vehicle had to be

rear wheel drive to meet the norms. Rear suspension needed to be spacious enough to accommodate engine

and provide some space for luggage compartment too. Passenger ride comfort was also a major driving

factor. This required a suspension design with softer springs. After a comparative study of solid axle, quad-

link, semi trailing arm type of suspension it was decide to go with semi trailing arm kind suspension as it

provided a balance between comfort and driving behavior. It also met the criteria of low cost and assembling

time. Solid axle kind would have required mounting of a separate differential and it was neither suitable for

engine nor for the light weight nature of vehicle.

3.2 Approach to CAD modelling and assembly of components.

Once finished with the type of suspension it was time to prepare the CAD model to evaluate and tune the

suspension as per the requirement. With the company’s vast database and experience in CAD modelling,

assembly process was quite convenient. Most of the component design and drawings were available in the

database. Whole vehicle design and assembly was carried out according to SAE convention.

According to SAE convention all points of interests were described as coordinates dimensioned from the

intersection of the zero planes in the three-dimensional reference system. XYZ coordinates were

dimensioned to their respective planes.

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Figure 9 Vehicle coordinate system in accordance with SAE convention

After fixing vehicle coordinate system assembly process started with fixing the wheel center and then

moving on to hub, knuckle and strut assembly. Static parameters like camber and toe were set to zero with

the option to change at later stage. It was decided to go with stock steering knuckle so the only choice of

altering or controlling kingpin inclination, scrub radius and caster was dependent on strut top mount. Hence

according to the requirement following suspension parameters were decided.

SUSPENSION

Tire Static Loaded Radius 0.261 m

Camber Angle 0.0 deg

Kingpin Inclination Angle 16.0 deg

Scrub Radius 0.002 m

Caster Angle 4.0 deg

Caster Trail 0.018 m

STEERING

Rack Stroke 0.160 m

Inner Steer Angle at Lock 50.4 deg

Outer Steer Angle at Lock 37.7 deg

Max. Ackerman Error 3.75 deg

Rack Force Ratio at Lock 1.6 -

Table 2 Suspension parameters

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The 12" wheel had an offset of 40 mm (ET) which allowed a better placement for the tie rod outer ball joint

inside the rim. The brake drum was positioned accordingly. In order to use the identical knuckle geometry

received from the database, the outer ball joint center location of the lower control arm was also modified.

Figure 9. Front suspension assembly

Taking into account, the tire SLR of 261 mm and the ground clearance target of 240 mm, the lowest design

position for the LCA inner pivot axis was kept at -95 mm in Z-axis initially.

The ideal position of the inner lower control arm attachment points was fixed on a line on the Y-Z plane,

which passed through the virtual swing arm rotation center of the MacPherson-type strut suspension. This

ensured that the suspension bump-steer was minimized. This was rechecked during toe control analysis.

For rear suspension the trailing arm pivot radius was kept 354 mm in order to accommodate the tire R12 tire.

In order to achieve sufficient amount of rear axle understeer during steady-state and yaw damping during

transient maneuvers, the pivot axis inclination was tuned to provide toe-in with increasing suspension

compression as per the preliminary idea.

Engine mounting points were decided based on the fact that CG should stay low and sufficient

ground clearance is also available. Drive shaft inner joint was also one of the factor while deciding engine

location as care was taken to keep CV joint angle to minimum for efficient power transfer. In static

condition CV joint had an angle of 10.83 deg. The tentative mounting of spring and dampers were

according to the packaging space which was subject to change as per the suspension analysis.

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Figure 10 Rear suspension assembly

3.3 Final representation of CAD model.

Figure 11 Final assembly top view

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Figure 12 Final assembly front view

Figure 13 Final assembly front ISO view

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After completing the full vehicle assembly in CAD, hardpoints were exported for modelling and analysis of

suspension design in Adams/car.

4. MODELING AND ANALYSIS IN ADAMS

4.1 Introduction to ADAMS/Car

Adams, developed by MSC Software Corporation is a multibody dynamics software that is widely used in

engineering industry. Adams/car is the part of Adams software suite and it provides a specialized

environment for modeling vehicles. The software formulates equations of motion based on absolute

coordinates to obtain a time response of the system. It can be time consuming as complex assemblies often

involve large systems of nonlinear differential algebraic equations requiring large amount of computing

power. Adams/car allows the user to create and test virtual prototypes of the vehicle subsystems and

complete vehicles much like the physical system. An extensive library of macros is also built into the

program to speed up the model creation. Using Adams, full vehicle assembly can be created /modified rapidly

and can be simulated for various conditions to understand their performance and behavior. Based on the

analysis result suspension geometry, spring rates and other kinematics can be altered in no time to get the

desired performance behavior. Since the main goal of this project is to design and study the suspension

system and vehicle behavior before building prototype, Adams was selected to perform this task.

Prior to modelling suspension system in Adams, an extensive study in vehicle dynamics, vector theory and

classical approach of designing was performed to understand the working of the software. It is of utmost

importance to understand what goes behind the screen and the working principle of this software. During the

study and modeling of the system it was found that if the user knows the working of the software then it

becomes very easy and efficient to modify the system and obtain desired results.

4.2 Working principle

The main analysis code consists of a number of integrated programs that perform three dimension

kinematic, static, quasi-static or dynamic analyses of the mechanical system. These programs form the core

of the solver. In addition to these a number of other programs are linked to the core solver which is used to

model vehicle tire characteristics, automatically generates vehicle suspension geometry etc. Once the model

is defined the core solver assembles the equation of motion and solves them. Possibility of inclusion of

differential equation in the solution makes it easier to model various control system. Complete Adams

working process has been explained in diagram.

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Figure 14 Integration of MSC. ADAMS with CAE software

The first step for simulation is to prepare a data set which defines the system. It includes rigid parts,

connecting joints, motion generators, forces and compliances. Adams provides the user to use various joints

and connectors used in the system.

For the real time similarity it is necessary that each rigid body’s mass, center of mass location and moment

of inertia is well defined. For simpler bodies Adams itself calculate all the above mentioned requirements.

For some complex components it was calculated in CAD and then manually entered in the software. Further

each body has a co-ordinates system which can be defined in local co-ordinate system or global co-ordinate

system. Parts and bodies move according to this definition during simulation. The relative motions

between different parts in the system are constrained using joints, gears, couplers etc.

The next step is defining the external and internal force elements. External forces can be constant, time

dependent function or any other state dependent function. These forces can be translational or rotational.

Internal forces act between two parts like spring, damper or rubber mounts. These are referred as action and

reaction forces and they always produce equal and opposite forces on two parts connected by the force

element.

Adams allows user to effectively access any displacement, velocity, acceleration or other force when

defining the force equation. Forces can also be switched on or off during simulation progress. Precaution

must be taken to ensure formulations are continuous in time domain to avoid any problem during the

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numerical solution of the resulting equations. If these forces or any other parameters are not in the given

range the solver is not able to execute the equation of motion resulting in failed simulation.

In Adams, vehicle suspension bushings and joints are represented by a set of six action and reaction forces,

which hold the two parts together. The equations of force are linear and uncoupled. Following the

common notion too much complexity is bad thing, Stiffness of the bushings and joints were mostly left

unaltered. A list of joints with their degrees of freedom has been updated in the following table.

Constraint

element(joint)

Translational

constraints

Rotational

constraints

Coupled

constraints

Total constraints

Cylindrical 2 2 0 4

fixed 3 3 0 6

Planar 1 2 0 3

Rack and pinion 0 0 1 1

Revolute 3 2 0 5

Spherical 3 0 0 3

Translational 2 3 0 5

Universal 3 1 0 4

Coupler 0 0 1 1

Table 3 Type of joints and their respective degrees of freedom

As per the real conditions, in Adams also, forces through the road are transferred to the tire. For each tire on

the model, Adams calculate the three orthogonal forces and torques acting at the wheel center as a result of

the condition at the tire road surface contact patch. It is resolved at the wheel center and then software

integrates it through time to find the new position and orientation of the vehicle and repeats the process.

In short suspension analysis can be explained with following diagram.

Figure 15 Steps of suspension analysis

In Adams suspension analysis is divided in two steps i.e., pre-processor and post processor. During first step

all input data is given through GUI or by command files and then solver performs the analysis. Post

processing is the second step in which all the results files are viewed. Post processor software is the part of

Adams suite and is used with other applications too. Post processor made it easy to understand the vehicle

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behavior. While looking to the model in motion it was easy to debug any anomaly. Post processor also

provided the option to perform mathematical operations and statistical analyses on plot curves. All the

results, simulations and presentation of curves were done in post processor.

4.3 Approach to system modeling

Since, it is quite clear that Adams/car is a powerful tool for simulation not modelling so, before starting the

modelling in Adams, it is highly suggested to sketch out a system schematics which would typically illustrate

the items such as parts, joints, imparted motion applied forces and its location. It also helps in predicting

degrees of freedom and develop a basic understanding how system will work. For the same reason detailed

CAD drawing was prepared and it made the modelling work less tedious to model the system in Adams.

Next step is to set up the reference frame. For a multibody three dimension description is required. It not

only set up the configuration and physical properties of the model but also to describe the calculated outputs

such as the displacement, velocities and acceleration. For the given model three types of reference frame co-

ordinate system was used.

4.3.1 Global reference coordinate This is the single inertial frame that is fixed and at rest. Any point defined to this reference frame has zero

velocity and acceleration. The ground reference is fixed on a body. For a single suspension model the ground

part may be taken to encompass the points on the vehicle body or sub-frame to which the suspension

linkages are attached. During a full vehicle modelling the ground part was related to the surface of road to

formulate the contact forces and moments in the tire model. It can be also considered as the origin of the

entire model. All other reference frames are measured relative to the ground reference frame.

4.3.2 Local coordinate system Each body or part has a local co-ordinate system which moves or changes according to the orientation of the

part. Adams takes it as body co-ordinate system. It is defined relative to the ground reference frame.

4.3.3 Markers These are the points located in the model to define the entities like mass center, position, spring ends etc. It

can belong to part or ground. Orientation of marker is important. For example in case of revolute joints,

marker should be along the axis of rotation or else joint will not behave as intended. The Euler angle method

can be used for orientation of the same.

Basic modeling components in ADAMS

Basic components are rigid bodies (part), geometry (marker), constraints (joints, gears etc.), forces (applied,

spring forces etc.), user defined algebraic and differential equations. Part statement will be used to define

rigid body or lumped mass. Suspension components like control arms, wheel, steering knuckle etc. will be

modelled as rigid bodies. For dynamic analysis full information like center of mass, moment of inertia,

orientation etc. is required.

4.4 Approach to system modeling

Adams works in two interfaces namely:

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4.4.1 Standard user interface In this mode standard templates are available (most commonly used designs) with all the required configuration, constraints and joints. It also facilitates the option of modifying various components, hard

points and several other parameters to create the desired geometry.

4.4.2 Template builder mode In this mode user need to enter all necessary data for the part to be created like role type, hard points, joints

, constraints, mass and inertia properties. It takes more time and effort than standard interface to create

desired template. It can be avoided if the type of geometry to be used is less complicated and more common.

But for creating a new geometry with desired properties and parameters it is always preferred.

For this particular study of the suspension system, choice was predefined as MacPherson for front and Semi

trailing arm for rear. Reasons for the same have been discussed in design of suspension section. Both

Macpherson and semi trailing arm suspension templates are available in Adams/car database. So it was

decided to go with standard user interface and modify the hard points, mass-inertia properties etc. to obtain

the desired configuration and geometry.

4.4.3 System modeling Steps to create a system model in Adams:

Creation of database and then selecting the working directory.

Then select “sub assembly” or “assembly” from file-new-menu

To obtain the complete vehicle model following assemblies and sub-assemblies were modeled and then finally assembled:

Front suspension assembly

Rear suspension assembly

Body and chassis

Powertrain assembly

Front and rear tires

4.4.4 Modeling of front suspension assembly Front suspension assembly consisted of 3 subassemblies: Suspension links with springs and damper, steering

system and test rig.

4.4.4.1 Modeling MacPherson suspension link subassembly for front

The template represented a standard design of one piece lower control arm and subframe. Upright was

represented by a combination of links to which hub, lower control arm, tie rod and strut was mounted. Fore-

aft and lateral motions of the uprights were regulated by the lower control arm. Steering rotation of the

upright was controlled by the tie rod and vertical, side, front view rotations were controlled by the strut.

During quasi-static analysis a static rotation control actuator locked the degree of freedom of the hub.

All the above mentioned parts were connected with different types of joints and bushings which has the

following topology explained in the table.

Main part Connecting part Type of joint.

Lower control arm Subframe Revolute joint

Upright Lower control arm Ball joint

Upright Upper strut Cylindrical joint

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Tie rod Upright Spherical joint

Tie rod tie rod to steering (mount part) Convel joint

Subframe Subframe to body (mount part) Fixed joint

Upper strut Strut to body (mount part) Hook joint

Spindle Upright Revolute joint

Table 4 Front parts and joints topology

Figure 16 MacPherson modelling component topology

After defining the topology, parameter variables were defined to incorporate any camber or toe in static

condition. In this case it was set to zero.

Parameter variable value unit

Camber 0 Deg.

Toe 0 Deg

Table 5 Static parameter variable table

For creating the assembly following steps were followed:

Step 1: Creating subassembly.

a) File—New—Subsystem

b) subsystem name : (Front_link_geometry)

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c) Minor role : Front

d) Template name : (Acar database _MacPherson.tpl file.)

Subassembly appeared on the screen.

Step 2: Modifying subassembly

Subassembly was modified using the hardpoints obtained from the CAD geometry. Refer Appendix 6.1

a) Select Adjust—Hardpoints—Table.

b) Following hardpoints were entered in the table. (As given in appendix) c) Spring preload and damper properties were also adjusted as per the requirement.

The following geometry was obtained:

Figure 17 Front suspension links

4.4.4.2 Modeling steering system subassembly

The type of steering to be modelled was rack and pinion. In the model rotatory motion of the steering wheel

was translated to linear motion by the pinion gear. The rack moved tie rods back and forth to steer the

vehicle. The motion from the steering to pinion was transferred by steering shafts which was connected with

a series of hook joints. Lower column shaft to the rack housing was connected by a revolute joint. Shaft to

the pinion was connected by a torsion bar bushing. Pinion to the rack housing was connected with the

revolute joint.

During kinematic mode, a reduction gear was active which connected the steering input shaft revolute joint to

the pinion revolute joint. The motion of rack to rack housing was constrained by a translation joint. In case

steering assist was required, it was given by VFORCE. Steer assist VFORCE was controlled by

steer_assis_.tbl file of the Adams/car database. In case steer assist was not needed it was switched off. All

parts and connection and joints topology can be summarized in the following table.

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Main Part Connecting part Type of joint

Steering column Intermediate shaft Hook joint

Intermediate shaft Steering shaft Hook joint

Rack Rack housing Translational joint

Steering wheel Steering column to body (mount part)

Revolute joint

Pinion Rack housing Revolute joint

Steering column Steering column to body(mount part)

Cylindrical joint

Steering shaft Rack housing Revolute joint

Rack housing Rack housing mount(switch part) Fixed joint

Table 6 Steering system joints topology

During analysis, switching between kinematic and complaint mode was carried out by the parameter

variable. It was set by the hidden option under parameter variable steering_assist_force. Maximum values of

steering angle, rack displacement, rack force and steering wheel torque was set using the same option.

Steps for creating steering subsystem has been described in following steps.

Step 1: Creating subassembly


b) Enter subsystem name : (Steering_system)

c) Minor role: Front

d) Template name: (Browse to Acar database and the select steering.tpl file.)

Subassembly appears on the screen.


Subassembly was modified using the hardpoints obtained from the CAD geometry.


b) Following hardpoints were entered in the table. (As given in appendix 6.2)

c) Steering gear ratio was also modified from the default value.

The following geometry was obtained.

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Figure 18 Steering links

4.4.4.3 Creating front suspension assembly

Once both front suspension links and steering subsystem was created and saved in template files, front

assembly was created in following steps.

a) File—New—suspension assembly.

b) Enter Assembly name (front_suspension_complete) c) Suspension subsystem (Browse and select Front_link_geometry file from subsystem.)

d) Select Steering subsystem (Browse and select Steering_system file from subsystem.)

e) Suspension Test Rig (select _MDI_SUSPENSION_TESTRIG) and apply.

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Figure 19 Front suspension assembly with test rig

4.4.5 Modeling rear suspension assembly Rear suspension assembly consisted of 2 subassemblies: Suspension links with springs and damper,

driveshaft system and test rig. The model to be created was semi trailing arm type suspension. It was non

steerable.

4.4.5.1 Modeling rear suspension link subassembly

In this model left and right trailing arms were connected to the rigid subframe and in turn subframe was

connected to body mount part through bushings. The wheel center was located by the arms. Spring and

damper act between arms and body mount parts. The rotational degree of freedom of the hub was locked by

the static rotational control actuator during quasi-static analysis. Joints and connection topology has been

summarized in the following table.

Main part Connecting part Type of joint

Strut to body (mount part) Upper strut Hook joint

Arm Subframe Revolute joint

Subframe Subframe to body (mount part) Fixed joint

Lower strut Arm Hook joint

Upper strut Lower strut Cylindrical joint

Spindle Arm Revolute joint

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Tripod Tripod to differential(mount part) Translational joint

Spindle Arm Revolute joint

Table 7 Rear assembly joints topology

For rear assembly too parameter variables were decided as explained in previous section for front

suspension. Static camber and toe values were kept zero. Complete model was created in following steps.

Step 1: Creating subassembly


b) Enter subsystem name: (Rear_link_geometry)

c) Minor role : Rear

d) Template name: (Browse to Acar database and the select trailingarm.tpl file. )

Subassembly appears on the screen.


Subassembly was modified using the hardpoints obtained from the CAD geometry as follows.


b) Following hardpoints were entered in the table. (As given in appendix)

4.4.5.2 Creating rear suspension assembly

Once the rear link template file was created and saved in database, complete assembly with the test rig was

created in following steps.

a) File—New—suspension assembly.

b) Enter Assembly name (Rear_suspension_complete)

c) Suspension subsystem (Browse and select Rear_link_geometry file from subsystem.)

Suspension Test Rig (select _MDI_SUSPENSION_TESTRIG) and apply.

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Figure 20 Rear suspension assembly with test rig

4.4.6 Body and chassis system Body and chassis system was modeled as single lump of mass which consisted of structural mass of body-in- white, engine, exhaust system, fuel tank, vehicle interior, driver, passenger and any other payload. Weight

distribution was done by editing trim part mass. The lump mass chassis had the limitation in terms of

torsional stiffness as it could not be defined in this kind of model. It required making several rigid bodies and

then connecting them with spring and damper to obtain the desired stiffness. Since evaluation chassis

stiffness was not the main goal of this study, it was left unchanged.

Chassis template was created in following steps.

Step 1: Creating subsystem.


b) Enter subsystem name: (Chassis_body)

c) Minor role: Any

d) Template name: (Browse to Acar database and the select rigid_chassis_lt.tpl file.)

Subsystem appears on the screen.


Subsystem was modified using the hardpoints obtained from the CAD geometry as follows.



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4.4.7 Powertrain assembly

Figure 21 Lumped mass body system

Powertrain assembly was modeled using standard template available in the database after modifying the

mounting points. Connection of engine to the drive shaft was verified and changed to chassis from ground. In

graphical representation it only shows the mounting point and drive shaft connection. Engine properties were

left unchanged except changing the mass.

Graph 1 Power train map

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Power train template had a very simple topology because it is just a functional representation of the engine.

The only rigid parts along with the engine body were differential outputs and revolute joints which

connected the rigid bodies to the engine body. Powertrain template was created in following steps.

Step 1: Creating subsystem


b) Enter subsystem name: (Power_train)

c) Minor role: Rear

d) Template name: (Browse to Acar database and the select Powertrain_lt.tpl file. )

Subsystem appears on the screen.


Subsystem was modified using the hardpoints obtained from the CAD geometry as follows.



Figure 22 Engine and powertrain system representation

4.4.8 Front and rear tyres modelling Three basic functions were being provided by the tire system. It supported vertical load, developed lateral

forces for cornering and longitudinal forces for acceleration and braking. The template consisted of wheel

parts rigidly connected to mount parts. The tire contact patch forces were transformed in forces and torques

applied at the hub. Force calculations were done by user defined sub routine files based on the tire properties.

Tire topology was defined by a fixed joint which connected the wheel part to the spindle mount part.

For better and ease of handling Pacejka2002.tir tire model was used. It was based on special version of

magic formula. It described the tire behavior for a smooth ride of frequency up to 8 Hz. It was also

suitable for a speed up to 30 Mph. Tire property file used has been added in the appendix.

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Figure 23 Front and rear tyres

4.4.9 Full vehicle assembly Once all the subsystems were created and saved in the respective database, full vehicle assembly was done.

Steps: Creating full vehicle assembly

a) File—New—Full vehicle assembly.

Required fields were filled as per the database templates shown below and the applied.

Figure 24 Database for full vehicle assembly

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Figure 25 Full vehicle assembly front view

Figure 26 Full vehicle assembly side view

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Figure 27 Full vehicle assembly top view

Figure 28 Full vehicle assembly Front-Iso

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4.5 Evaluation of suspension and steering characteristics In Adams/car during suspension analyses, a total of 38 characteristics (Camber, toe, roll, caster etc.) are

calculated. Force limit for the left and right test rig jack is -2.0e+04 and 4.0e+04 N. This force limit can be

modified while working in the template builder mode, using ‘define actuator’ option.

The suspension and steering characteristics that Adams/car computes are based on the suspension geometry,

suspension compliance matrix or both. Suspension geometry refers to the position and orientation of

suspension parts relative to ground as the suspension is articulated through its ride, roll and steer motion.

Suspension compliance matrix refers to incremental movements of the suspension due to the application of

incremental forces at the wheel center. Throughout the motion, at each position Adams compute the

compliance matrix. Characteristics such as suspension ride and camber aligning torque are the result of

compliance matrix.

4.5.1 Definition of complex matrix Compliance matrix is the partial derivative of displacement with respect to applied forces.

If the system is assumed to be linear, then its movement can be prescribed with the applied force.

Here, matrix element Cij is the displacement of system, degree of freedom I due to a unit force at degree of

freedom j.

Adams uses a 12x12 matrix relating the motion of the left and right wheel centers to unit forces and torques

applied to the wheel centers. It has the following form:

Figure 29 Compliance matrix

Further for calculating characteristics such as camber, caster, scrub, caster moment arm etc. Adams uses

steering axis of the suspension. User has two method available i.e geometric method and instant axis method.

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Geometric method: The steer axis is calculated by passing a line through the selected points. Generally it is

suitable for solid axle suspension.

Instant axis method: To calculate the steer axis at a given position, Adams/car first locked the spring travel

and applied an incremental steering torque or force in all directions. Then from the resulting translation and

rotation of the wheel carrier part instant axis of rotation for each wheel was calculated.

For this particular suspension instant axis method of calculation was selected.

4.5.2 Wheel travel analysis The wheel travel analysis allowed to see, how the suspension characteristics changed throughout the vertical

range of motion. Adams/car provided option of three kinds of wheel analysis i.e parallel, opposite, single

wheel analysis. First two were sufficient to evaluate the characteristics and has been discussed in detail in

following sections.

4.5.2.1 Parallel and opposite wheel travel analysis

These wheel travel analysis were performed to check the behavior of vehicle kinematic parameters when

both wheel went in jounce and rebound condition simultaneously or in opposite direction. Opposite wheel

motion simulated body in roll condition. Main factors which were under investigation were change in

camber, toe, kingpin inclination, and track radius and track width.

Before running test, the parameters like tire model, tire stiffness, wheelbase, sprung mass, CG height, wheel

mass were defined. Once the suspension parameters were fixed, analysis parameters were defined. During

the analysis, the test rig applied forces or displacement or both to the assembly as defined in a load case file.

Adams/car generated a temporary load case file based on the input given which was used for future

simulations.

Test parameters:

Suspension assembly : Final_front / Rear_assembly

Output Prefix : PWT_front / PWT_Rear

Number of steps : 150

Mode of simulation : Interactive

Vertical setup Mode : Wheel center

Bump Travel : 80

Rebound travel : -60

Travel Relative To : Wheel center

Control mode : Absolute

The camber change observed for front in the beginning with the base geometry was in access of ±3.2º. This

high camber change was not acceptable as that would lead to large chassis roll and loss of tire contact patch

area, leading to excessive tire wear. It needed modification, so a design of experiment was carried out using

Adams/Insight to find out the most critical factors. After the experiment, it was observed that Z-component

of lower front control arm pivot point and lower control arm outer ball joints were the major contributing

factors, evident from the following figure.

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Figure 30 Camber change Design of Experiment

Finally a camber change of 2.4º was achieved. The change was still large so a compromise was done to

maintain the target ground clearance, because changing the Z-component of lower control arms would move

the vehicle further close to the ground.

Further a change in sign for toe was also observed which would result in unfavorable side drift/jerk during

jounce and rebound conditions.

Graph 2 Observed toe with sign change

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During toe correction investigation (Fig .25) it was observed that the tie rod joints rotation arc during wheel

travel were slightly deviated from the wheel rotation arc. Hence using the geometry, inner and outer tie rod

ball joint coordinates were modified to follow the same arc of rotation as that of wheel travel. Finally desired

toe change with the same sign was achieved as shown in graph 2.

Graph 3 Toe adjustment geometry

Graph 4 Modified toe with negligible sign change observed

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Graph 5 Caster and KPI v/s wheel travel curve

For a parallel wheel travel of +80mm and -60mm a maximum caster change of 2.4° was observed. It was

good to control dynamic camber change and for straight line stability. It was also expected to provide good

self-aligning torque during full vehicle simulations. Moreover large caster change would also lower the ride

height of the vehicle and suspension will have to be stiffen causing ride discomfort but in this case it stayed

within limit. For KPI, the analysis started with static value of 16°. But later it was reduced to 11° to control

the camber change. Though with the smaller KPI there was an increase in scrub radius but it provided a good

steering feel and balanced cornering performance.

Graph 6 Front track change v/s wheel travel

The observed track change for the front was ±12mm for a wheel travel of +80mm to -60mm. It did not

create any major effects on vehicle dynamics. Large track change would led to increase in rolling resistance

and excessive tyre wear.

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Graph 7 Rear track change v/s wheel travel

For rear suspension there was a track change of ±3.5 mm. It was quite small and well within the expected

range.

4.5.3 Steering analysis

This test was performed to check vehicle kinematic behavior when it is steered. It simulates the condition of

vehicle in turn or going around a corner. The target of this steering system is to have a short turning radius,

good Ackerman geometry and a better response.

In steering analysis the wheel is steered over the specified wheel angle or rack travel displacement from the

upper to the lower bound. All the parameters are evaluated for the condition when vehicle is at very low

speed and free of any lateral forces. The application of steering motion results in a wheel displacement at a

specified wheel height. For performing this analysis a steering system, suspension subsystem and test rig is

required.

Test parameters:

Suspension assembly : Final_front

Output Prefix : Steering analysis

Number of steps : 150

Mode of simulation : Interactive

Vertical setup Mode : Wheel center

Upper steer limit : 80

Lower steer limit :-80

Control mode : Absolute

Steer Input : Length

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Graph 8 Steer angle vs rack displacement

For a rack displacement of ±80mm maximum ideal steer angle of 38° was obtained at inside wheel with the

Ackerman geometry. The target for minimum turning radius was 3.65m and with the maximum steer angle,

it was achieved.(Graph 8). Larger steer angle forces the wheel arch to move inside and due to which pedal

assembly would not be in straight line with the driver foot. But in this case ideal steer angle being less than

40º there was less space needed for wheel envelop thus full filling the criteria of large front cabin space and

there was no problem of driver leg and pedal alignment. It also provided enough space to mount snow chains

if needed.

Graph 9 Turn radius

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Graph 10 Ackerman error

4.6 Full vehicle simulation For full vehicle simulation all previously created subsystems were assembled and complete vehicle model

was prepared as explained during system modeling. During this analysis it was planned to evaluate different

subsystem and to observe how they influence the total vehicle dynamics. This simulation also facilitated the

option of examining the influence of component modifications, change in spring and damper rates. Except

the data driven analysis, it was planned to use MDI_SDI_TESTRIG which were based on driving machine.

In Adams/car during full vehicle simulation, vehicle was driven by driving machine much like a test driver

would do on given instructions. The driving machine steered the vehicle, applied throttle, brake and shifted

gear using clutch as per the values entered. It was also possible to instruct driving machine to switch between

machine control and smart driver option.

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Figure 31 Driving machine function

4.6.1 Straight line maintain test

This test is part of the handling and ride analysis of the vehicle. Long driving makes driver feel tired due to

continuous steering correction. It is performed to check the ability of the vehicle to drive in a straight line.

This nomenclature traditionally used is just perceptual one but not from its physical definition. This test

usually represents comfort but in worst case safety. It is generally assessed through the evaluation of four

characteristics such as residual pull, running straight, torque steer, braking straight. The following test was

performed to check for the ability to drive in straight line without any drift, sloppiness with fixed steering

and constant speed. During full vehicle modeling these tests are run in the beginning to check if all the joints

and connectors are attached properly and model is test worthy or not. It also gives an idea regarding the

sensitivity of steering and suspension system against road irregularities or wind disturbances.

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Figure 32 Vehicle straight line test set-up

The test was run with constant speed and throttle. Steering input was locked. Mode of test was quasi-static

straight line. During the test in the beginning Adams lock the body’s fore-aft and lateral position using

primitive joint. It also tried to keep the vehicle’s yaw rate and lateral acceleration zero. To remove the effect

of any aerodynamic drag and scrub produced by the tyre, the throttle or brake will be adjust ed to match the

initial acceleration. Once the vehicle settles down, it will deactivate the primitive joint before executing the

maneuver. Finally the vehicle is allowed to run according to its geometry.

Test parameters

a) Initial velocity : 50kmph

b) Steering Input : Locked

c) Throttle control : Constant

d) Gear : 4th

e)

f)

Road type

Analysis type

: Flat

: Quasi static

Graph 11 Longitudinal vs lateral displacement

For a straight line travel of more than 200m there was negligible lateral displacement. This shows vehicle

has a good straight line driving behavior and in terms of handling it will be quite comfortable.

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Graph 12 Front steering angle

Front steering angle vs time graph shows there was no need to adjust steering during the maneuver. Little

vibration is observed just after the start but that is the time when driving machine settles down the vehicle

and prepare for the maneuver.

Graph 13 Inclination angle vs time

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Graph 14 Lateral force vs time

The camber angle change was same for both set of left and right tires. Lateral forces generated in tires were

cancelled being equal and opposite both in front and rear. Thus it was concluded that vehicle has a good

weight distribution and symmetric set up. It is capable of driving in straight line without much steering

correction and is ready for further tests.

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4.7 Single Iso-lane change maneuver This maneuver is most operated handling maneuver on highways and public roads. The purpose of this

maneuver is to overtake a vehicle appearing infront on a highway or to avoid running over an object/obstacle

appearing suddenly. Since vehicle changes one lane it is called single lane change. While changing lane both

stability and controllability are mainly evaluated by studying steering and yaw characteristics.

Figure 33 Single and double lane change

In this analysis, the driving machine drives the full vehicle through a lane change as specified in ISO-single

lane change document. During analysis, a longitudinal controller maintains the chassis velocity as specified

and later controller module acts on the steering system to maintain the vehicle on the desired lane change

path. Iso_lane_change.dcd file is used to define the manuever and trace on the XY-Plane. This test was

performed for three speeds.

Test procedures:

a) Experiment Name : ISO-Lane change

b) Static setup : Straight

c) Initial speed : 50, 55, 60 kmph

d) Gear Position : 3

e) Step size : 0.01

f) Distance : 250 m

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Graph 15 Chassis displacement

This test was repeated for three different speeds 50, 55, 60 kmph respectively to evaluate vehicle yaw

behavior. During simulation vehicle did change lane successfully within given parameter but at the end of

maneuver it drifted slightly laterally, evident from above figure. This drift was progressive with the increase

in vehicle speed. That means in real situation by the end of maneuver driver will have to do the steering

correction to bring the vehicle back in straight line.

Graph 16 Yaw rate and steering wheel angle at 50kmph

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From the above 3 curves it was observed that at 50 Kmph vehicle’s yaw rate, steer angle and lateral

acceleration were in good phase but as speed increased this phase difference became evident. This difference

in phase depicts that vehicle is not going in the direction where steering points, rather it is drifting away and

it can be dangerous at high speed. Though the phase difference is not very large and vehicle has a top speed

of 70 kmph, the extreme situation is not expected and it will be safe during the maneuver.

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4.8 Ramp steer

The main purpose of this test is to evaluate the understeer behavior of the vehicle while negotiating a turn.

To simulate the same condition it is planned to run the vehicle in spiral path (as shown in fig.) at constant

speed while changing the radius at constant rate.

Vehicle entry path

Figure 34 ramp steer test

During this analysis, Adams/car ramps up the steering input from an initial value at a specific rate, which in

this case was 5deg/sec. At the end of this test a time-domain transient response metrics is obtained. The most

important quantities which are to be measured include steering wheel angle, yaw rate, vehicle speed, lateral

acceleration and maneuver radius. All these quantities will be used to evaluate the steering behavior. As

Adams/car does not have a default request inbuilt to evaluate understeering characteristics hence it was

calculated in excel manually with the obtained data of steering wheel angle and maneuver radius.

Test parameters:

Figure 35 Ramp steer test parameters

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Along with the above parameters a separate event was created using event builder option to keep the velocity

constant and steering input changing. First simulation was done with normal conditions then the generated

.xml file was edited to have the desired driver input of keeping speed constant.

Figure 36 Event builder

As the understeer curve is not directly calculated in Adams/car a separate excel file was generated. To

calculate the steer angle at ground a separate simulation for steering system was done in static condition.

Correlating factor between wheel and steering was calculated from the same. It was then multiplied with the

values of steer angle of ramp steer analysis to get the mean steer angle in dynamic condition and then plotted

against L/R.

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Graph 19 Steering wheel angle v/s lateral acceleration

From the above graph of lateral acceleration vs steer wheel angle it is evident that as the turning radius was

getting smaller with each step, lateral accelration was continuosly increasing and it went till a limit of 0.9g

after which vehicle was not able to compensate for lateral forces and it started sliding causing a decreasing

trend in lateral acceleration even while steer angle was kept increasing.

Graph 20 Turning radius v/s steer wheel angle

The simulation started with a zero steer angle and a constant ramp steer of 5deg/s was given. This rapidly

reduced the cornering radius to a smaller value of 30m by the end of maneuver required to bring the vehicle

in unstable state.

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Graph 21 Yaw rate v/s steer wheel angle

For the first 10sec of maneuver change of yaw rate was in coherence with the steer angle but as it kept

increasing, yaw rate became constant suggesting vehicle was now sliding away from the path.

Graph 22 Velocity v/s steer wheel angle

To evaluate the steering characteristics, this maneuver had to be constant speed but Adams driver was trying

to keep the vehicle in stable state hence it was decreasing the velocity. Driver control file was modified to

keep the vehicle constant at all time and a constant velocity maneuver was obtained.

59

Me

an s

teer

an

gle

'δ' (

rad

)

Understeer_curve

0.12

0.1

0.08

dδ/(dL/R)=1 dδ/(dL/R)=0

1 2 3

Unstable

0.06

0.04

L/R

dδ/(dL/R)=1

dδ/(dL/R)=0

0.02

0

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28

L/R

Graph 23 Understeer curve

From above figure it is observed that vehicle has understeer characteristics in zone 1 as turning radius is

large enough to compensate for lateral forces and as radius decreases it becomes over steer. Further the

driving machine keeps the velocity constant while turning radius is decreased and cornering conditions are

getting sever with each step. Due to this lateral acceleration reaches a level beyond which it cannot be

compensated by lateral weight shift on tires and after that it goes in the unstable state. The point of unstable

state is far severe than the normal driving conditions hence it was concluded that vehicle is safe during

cornering and it would follow the path desired by the driver.

60

5. Conclusion MSC Adams/Car was selected as multi-body dynamics software for this study and to predict the behavior in

various dynamic conditions without any need of physical test data. A full vehicle model was successfully

created with the input from CAD model and from the data provided by the OEM.

Prior to the modelling in ADAMS, detailed CAD models were prepared according to the market survey and

target values. For preparing the CAD model, company’s CAD database was extensively used. This provided

more time to focus on multi-body system study.

Modelling process was carried out in ADAMS/car 2014 version. Complete model was divided into

subsystems, like front suspension, rear suspension, body and powertrain. Front MacPherson suspension and

rear semi trailing arm suspension were created by modifying the hardpoints and changing other parameters.

Those parameters which were unknown like spring damper rate and weight distribution were either estimated

or left to default values.

To improve the accuracy of the complete model, each subsystem was individually evaluated and tuned.

Parallel and opposite wheel travel analysis was done for both front and rear suspension subsystem.

Unexpected behavior was addressed at subsystem level and any compromises made were documented to

study its effects during full vehicle simulation.

During full vehicle analysis, vehicle was evaluated for straight line stability, lane change and ramp steer

behavior. Vehicle had a very good straight line driving capability. During lane change test at high speed,

vehicle performance was satisfactory as it was deviating from the path and additional steering corrections

were needed. In ramp steer maneuvers vehicle was forced to go in unstable condition which required high

velocity and shorter turning radius. This condition was not expected in real situation.

So conclusively in terms of ride and handling behavior in normal driving conditions, vehicle had good

capabilities. It was worth to prepare a prototype in accordance with the result obtained from the study. For

future works it would be quite useful to perform a four-post test rig analysis and kinematic & compliance

analysis to further assess and optimize tire, suspension parameter and ride comfort of passengers.

61

6. Appendix

6.1 Front assembly hardpoints.

Hardpoint name Symmetry X value Y value Z value

Lca front Left/right 254 -200 -95

Lca outer Left/right 250.2 -609.3 -162.9

Lca rear Left/right 554 -200 -75

Spring lower seat Left/right 267.28 -548 110

Strut lower mount Left/right 257.5 -603.0 -58

Subframe front Left/right -250 -200 -75

Subframe rear Left/right 1000 -200 -75

Tierod inner Left/right 200 -248 -55

Tierod outer Left/right 127 -617.7 -109

Top mount Left/right 291.9 -438 429.7

Wheel center Left/right 254 -670 -109

6.2 Steering system


Intermediate shaft forward

Single 208.13 101.7 162.63

Intermediate shaft rearward

Single 357.62 238.5 422.6

Pinion pivot Single 200.0 -9.59 -55.0

Steering wheel center Single 661.4 248.02 697.81

Rack house mount Left/right 200.0 -238.0 -55.0

Tierod inner Left/right 200.0 -238.0 -55

6.3 Rear suspension system


Subframe fixed Single 0 0 150

Arm inner pivot Left/right 1765 -358 -71

Arm outer pivot Left/right 1749 -682 -89

Arm strut bushing Left/right 2100 -600 -71

Arm strut bushing x Left/right 1700 -555 -71

Arm strut bushing z Left/right 1749 -682 -71

62

Drive shaft inner Left/right 2054 -120 -2

Spring lower seat Left/right 1950 -590 -71

Spring upper seat Left/right 1950 -590 -71

Subframe front Left/right 1500 -682 -89

Subframe rear Left/right 2200 -600 300

Top mount Left/right 2200 -600 300

Wheel center Left/right 2054 -670 -109

6.4 Body subsystem

Hardpoint name Symmertry X value Y value Z value

Path reference Single 0 0 0

Trim dummy Single 852 0 -2.0

Front whel center Left/right 254 0 -2.0

Rear wheel center Left/right 2054 0 -2.0

6.5 Powertrain subsystem

Hard point name Symmetry X value Y value Z value

Graphics reference Single 2000 -90 610 Front engine mount Left/right 1900 -358 -71

Rear engine mount Left/right 2200 -358 -71

6.6 Tire property file.

[MDI_HEADER]

FILE_TYPE ='tir'

FILE_VERSION =3.0

FILE_FORMAT ='ASCII'

! : TIRE_VERSION : PAC2002

! : COMMENT : Tire 175/70 R13

! : COMMENT : Manufacturer

! : COMMENT : Nom. section with (m) 0.175

! : COMMENT : Nom. aspect ratio (-) 0.80

! : COMMENT : Infl. pressure (Pa) 190000

! : COMMENT : Rim diameter (inch) 12

! : COMMENT : Measurement ID

! : COMMENT : Test speed (m/s) 16.7

! : COMMENT : Road surface

! : COMMENT : Road condition Dry

! : FILE_FORMAT : ASCII

! : Copyright (C) 2004-2011 MSC Software Corporation

!

! USE_MODE specifies the type of calculation performed:

! 0: Fz only, no Magic Formula evaluation

! 1: Fx,My only

! 2: Fy,Mx,Mz only

63

VERTICAL_STIFFNESS

VERTICAL_DAMPING

=

=

1.75e+005

50

$Tyre vertical stiffness

$Tyre vertical damping

BREFF = 7 $Low load stiffness e.r.r.

DREFF = 0.25 $Peak value of e.r.r.

FREFF = 0.01 $High load stiffness e.r.r.

FNOMIN = 3800 $Nominal wheel load

! 3: Fx,Fy,Mx,My,Mz uncombined force/moment calculation

! 4: Fx,Fy,Mx,My,Mz combined force/moment calculation

! +10: including relaxation behaviour

! *-1: mirroring of tyre characteristics

!

! example: USE_MODE = -12 implies:

! -calculation of Fy,Mx,Mz only

! -including relaxation effects

! -mirrored tyre characteristics

!

$----------------------------------------------------------------units

[UNITS]

LENGTH ='meter'

FORCE ='newton'

ANGLE ='radians'

MASS ='kg'

TIME ='second'

$----------------------------------------------------------------model

[MODEL]

PROPERTY_FILE_FORMAT ='PAC2002'

USE_MODE = 14 $Tyre use switch (IUSED)

VXLOW = 1

LONGVL = 16.7 $Measurement speed

TYRESIDE = 'LEFT' $Mounted side of tyre at

vehicle/test bench

$-----------------------------------------------------------dimensions

[DIMENSION]

UNLOADED_RADIUS = 0.29 $Free tyre radius

WIDTH = 0.175 $Nominal section width of

the tyre

ASPECT_RATIO = 0.8 $Nominal aspect ratio

RIM_RADIUS = 0.165 $Nominal rim radius

RIM_WIDTH = 0.127 $Rim width

$----------------------------------------------------------------shape

[SHAPE]

{radial width}

1.0 0.0

1.0 0.4

1.0 0.9

0.9 1.0

$------------------------------------------------------------parameter

[VERTICAL]

$------------------------------------------------------long_slip_range

[LONG_SLIP_RANGE]

KPUMIN = -1.5 $Minimum valid wheel slip

KPUMAX = 1.5 $Maximum valid wheel slip

$-----------------------------------------------------slip_angle_range

[SLIP_ANGLE_RANGE]

ALPMIN = -1.5708 $Minimum valid slip angle

ALPMAX = 1.5708 $Maximum valid slip angle

$-----------------------------------------------inclination_slip_range

[INCLINATION_ANGLE_RANGE]

CAMMIN = -0.26181 $Minimum valid camber angle

64

CAMMAX = 0.26181 $Maximum valid camber angle

$-------------------------------------------------vertical_force_range

[VERTICAL_FORCE_RANGE]

FZMIN = 190 $Minimum allowed wheel load

FZMAX = 8250 $Maximum allowed wheel load

$--------------------------------------------------------------scaling

[SCALING_COEFFICIENTS]

LFZO = 1 $Scale factor of nominal

(rated) load

LCX = 1 $Scale factor of Fx shape

factor

LMUX = 1 $Scale factor of Fx peak

friction coefficient

LEX = 1 $Scale factor of Fx

curvature factor

LKX = 1 $Scale factor of Fx slip

stiffness

LHX = 1 $Scale factor of Fx

horizontal shift

LVX = 1 $Scale factor of Fx vertical

shift

LGAX = 1 $Scale factor of camber for

Fx

LCY = 1 $Scale factor of Fy shape

factor

LMUY = 1 $Scale factor of Fy peak

friction coefficient

LEY = 1 $Scale factor of Fy

curvature factor

LKY = 1 $Scale factor of Fy

cornering stiffness

LHY

horizontal

shift

= 1 $Scale factor of Fy

LVY

shift = 1 $Scale factor of Fy vertical

LGAY

Fy = 1 $Scale factor of camber for

LTR = 1 $Scale factor of Peak of

pneumatic

LRES

trail =

1

$Scale

factor

for offset of

residual torque LGAZ = 1 $Scale factor of camber for

Mz

LXAL

=

1

$Scale

factor

of

alpha

influence on

LYKA

Fx =

1

$Scale

factor

of

alpha

influence on Fx LVYKA

induced Fy = 1 $Scale factor of kappa

LS

of Fx = 1 $Scale factor of Moment arm

LSGKP

length of Fx = 1 $Scale factor of Relaxation

LSGAL

length of Fy = 1 $Scale factor of Relaxation

LGYR = 1 $Scale factor of gyroscopic

torque

LMX

=

1

$Scale

factor

of

overturning

couple

65

LVMX = 1 $Scale factor of Mx vertical

shift

LMY

= 1

$Scale factor of rolling

resistance torque $---------------------------------------------------------longitudinal

[LONGITUDINAL_COEFFICIENTS]

PCX1 = 1.5587 $Shape factor Cfx for

longitudinal force

PDX1 = 1.09 $Longitudinal friction Mux

at Fznom

PDX2 = -0.079328 $Variation of friction Mux

with load

PDX3 = 9.9376e-006 $Variation of friction Mux

with camber

PEX1 = 0.27403 $Longitudinal curvature Efx

at Fznom

PEX2 = 0.10232 $Variation of curvature Efx

with load

PEX3 = 0.074903 $Variation of curvature Efx

with load squared

PEX4 = -0.00026944 $Factor in curvature Efx

while driving

PKX1 = 19.733 $Longitudinal slip stiffness

Kfx/Fz at Fznom

PKX2 = 0.093405 $Variation of slip stiffness

Kfx/Fz with load

PKX3 = 0.12433 $Exponent in slip stiffness

Kfx/Fz with load

PHX1 = -0.001779 $Horizontal shift Shx at

Fznom

PHX2 = 0.00021808 $Variation of shift Shx with

load

PVX1 = -9.9052e-006 $Vertical shift Svx/Fz at

Fznom

PVX2 = -2.8568e-005 $Variation of shift Svx/Fz

with load

RBX1 = 14.927 $Slope factor for combined

slip Fx reduction

RBX2 = -10.534 $Variation of slope Fx

reduction with kappa

RCX1 = 1.1288 $Shape factor for combined

slip Fx reduction

REX1 = 0.62334 $Curvature factor of

combined Fx

REX2 = -0.0039079 $Curvature factor of

combined Fx with load

RHX1 = 0.001683 $Shift factor for combined

slip Fx reduction

PTX1 = 1.9021 $Relaxation length

SigKap0/Fz at Fznom

PTX2 = -0.0014739 $Variation of SigKap0/Fz

with load

PTX3 = 0.03631 $Variation of SigKap0/Fz

with exponent of load

$----------------------------------------------------------overturning

[OVERTURNING_COEFFICIENTS]

QSX1 = 0 $Lateral force induced

overturning moment

66

QSX2 = 0 $Camber induced overturning

couple

QSX3

= 0

$Fy induced overturning

couple $--------------------------------------------------------------lateral

[LATERAL_COEFFICIENTS]

PCY1 = 1.4675 $Shape factor Cfy for

lateral forces

PDY1 = 0.94002 $Lateral friction Muy

PDY2 = -0.17669 $Variation of friction Muy

with load

PDY3 = -0.69602 $Variation of friction Muy

with squared camber

PEY1 = 0.0040023 $Lateral curvature Efy at

Fznom

PEY2 = 0.00085719 $Variation of curvature Efy

with load

PEY3 = 41.465 $Zero order camber

dependency of curvature Efy

PEY4 = 665.25 $Variation of curvature Efy

with camber

PKY1 = -12.536 $Maximum value of stiffness

Kfy/Fznom

PKY2

maximum value

= 1.3856 $Load at which Kfy reaches

PKY3 = -0.93342 $Variation of Kfy/Fznom with

camber

PHY1

=

0.0024749

$Horizontal shift Shy at

Fznom

PHY2

=

0.0037538

$Variation of shift Shy with

load PHY3

camber

= 0.037561 $Variation of shift Shy with

PVY1

Fznom

= 0.031255 $Vertical shift in Svy/Fz at

PVY2

with load

= -0.0017359 $Variation of shift Svy/Fz

PVY3 = -0.38166 $Variation of shift Svy/Fz

with camber

PVY4

=

-0.033117

$Variation of shift Svy/Fz

with camber and load

RBY1

=

5.5228

$Slope factor for combined

Fy reduction

RBY2

=

2.7966

$Variation of slope Fy

reduction with alpha

RBY3

=

0.08688

$Shift term for alpha in

slope Fy reduction RCY1

Fy reduction

= 1.0783 $Shape factor for combined

REY1

combined Fy = 0.055543 $Curvature factor of

REY2

combined Fy

with load

= -0.0022958 $Curvature factor of

RHY1

Fy reduction = -0.0027141 $Shift factor for combined

RHY2 = -0.00098972 $Shift factor for combined

Fy reduction

RVY1

with load =

0.0076305

$Kappa induced side force

Svyk/Muy*Fz at Fznom

67

RVY2

with

load

= -0.09933 $Variation of Svyk/Muy*Fz

RVY3 = 0.16991 $Variation of Svyk/Muy*Fz

with

RVY4

camber =

-9.6324e-005

$Variation

of

Svyk/Muy*Fz

with alpha RVY5

with

kappa

= 1.9 $Variation of Svyk/Muy*Fz

RVY6

with

atan(kappa)

= 0 $Variation of Svyk/Muy*Fz

PTY1

length

SigAlp0/R0

= 1.8473 $Peak value of relaxation

PTY2 = 1.9465 $Value of Fz/Fznom where

SigAlp0 is extreme

$---------------------------------------------------rolling resistance

[ROLLING_COEFFICIENTS]

QSY1 = 0.01 $Rolling resistance torque

coefficient

QSY2 = 0 $Rolling resistance torque

depending on Fx


depending on speed


depending on speed ^4

$-------------------------------------------------------------aligning

[ALIGNING_COEFFICIENTS]

QBZ1 = 9.2824 $Trail slope factor for

trail Bpt at Fznom

QBZ2 = -2.6095 $Variation of slope Bpt with

load


load squared


camber


absolute camber

QBZ9 = 13.946 $Slope factor Br of residual

torque Mzr

QBZ10 = 0 $Slope factor Br of residual

torque Mzr

QCZ1 = 1.1119 $Shape factor Cpt for

pneumatic trail

QDZ1 = 0.14332 $Peak trail Dpt" =

Dpt*(Fz/Fznom*R0)

QDZ2 = -0.0062385 $Variation of peak Dpt" with

load


camber


camber squared

QDZ6 = -0.0073867 $Peak residual torque Dmr" =

Dmr/(Fz*R0)

QDZ7 = 0.0016767 $Variation of peak factor

Dmr" with load

QDZ8 = -0.17212 $Variation of peak factor

Dmr" with camber

QDZ9 = -0.033444 $Variation of peak factor

Dmr" with camber and load

68

QEZ1 = -2.9203 $Trail curvature Ept at

Fznom

QEZ2 = -0.91079 $Variation of curvature Ept

with load

QEZ3 = 0 $Variation of curvature Ept

with load squared

QEZ4 = 0.32935 $Variation of curvature Ept

with sign of Alpha-t

QEZ5 = -1.9083 $Variation of Ept with

camber and sign Alpha-t

QHZ1 = 0.0019422 $Trail horizontal shift Sht

at Fznom

QHZ2 = 0.0034645 $Variation of shift Sht with

load

QHZ3 = 0.14727 $Variation of shift Sht with

camber

QHZ4 = -0.035133 $Variation of shift Sht with

camber and load

SSZ1 = 0.026243 $Nominal value of s/R0:

effect of Fx on Mz

SSZ2 = -0.013391 $Variation of distance s/R0

with Fy/Fznom

SSZ3 = 0.3923 $Variation of distance s/R0

with camber

SSZ4 = -0.16022 $Variation of distance s/R0

with load and camber

QTZ1 = 0.2 $Gyration torque constant

MBELT = 3.5 $Belt mass of the wheel

$-----------------------------------------------contact patch parameters

! 3D contact can be switched on by deleting the comment ! character

! When no further coefficients are specified, default values will be taken

![CONTACT_COEFFICIENTS]

CONTACT_MODEL = '3D_ENVELOPING'

REFERENCES [1] The Multibody Systems Approach to Vehicle Dynamics, Mike Blundell and Damian Harty

[2] Tune to win, by Caroll smith

[3] Fundamentals of Vehicle Dynamics- by Gillespie

[4] Jazar - Vehicle Dynamics - Theory and Application (Springer, 2008)

69

[5] Road and off-road vehicle system dynamics handbook, edited by- Giampiero Mastinu and Manfred

Ploechl

[6] Race car vehicle dynamics – Milliken and Milliken

[7] Subjective Evaluation and Vehicle Behavior in Lane-Change Maneuvers

[8] http://mech.unibg.it/~lorenzi/VD&S/Matlab/Tire/tire_models_pac2002.pdf

[9]

http://www.researchgate.net/publication/265323638_Technical_Report_on_Virtual_Prototyping_of_G

round_Vehicles

[10] http://paws.kettering.edu//~amazzei/student_guide.pdf

[11]

http://www.researchgate.net/publication/268351344_Simulation_analysis_and_optimization_design_o

f_front_suspension_based_on_ADAMS

[12] http://link.springer.com/article/10.1007%2FBF02982435

[13] http://www.tandfonline.com/doi/abs/10.1080/00423110801956232

[14] http://www.sciencedirect.com/science/article/pii/S0094114X07000213

[15]https://www.scribd.com/doc/25487188/Using-Adams-PostProcessor-MD-Adams-2010

[16] http://forums.mscsoftware.com/adams/postlist.php?Cat=&Board=car

[17] https://simcompanion.mscsoftware.com/infocenter/index?page=home

[18] https://law.resource.org/pub/us/cfr/ibr/005/sae.j1100.2001.html

[19]file:///C:/MSC.Software/Adams_x64/2014/help/adams_car/wwhelp/wwhimpl/js/html/wwhelp.htm#hre

f=welcome.html

[20] http://www.fsae.com/forums/forumdisplay.php?45-Open-FSAE-Discussion

[21] http://www.eng-tips.com/viewthread.cfm?qid=389983

[22] http://www.millikenresearch.com/rcvd.html

[23] http://www.f1technical.net/forum/

[24] http://papers.sae.org/800845/

[25]http://www.sae.org/servlets/product%3BWebLogicSession%3FPROD_TYP%3DSTD%26PARENT_BPA_C

D%3DGV%26TECH_CD%3DTIRES

[26] http://www.optimumg.com/technical/technical-papers/

[27] https://uwspace.uwaterloo.ca/handle/10012/7824

[28]https://antonaengineering.files.wordpress.com/2012/11/jon_fernandez_de_antona_beng_project_exc

erpt3.pdf

http://mech.unibg.it/~lorenzi/VD&S/Matlab/Tire/tire_models_pac2002.pdf

http://www.researchgate.net/publication/265323638_Technical_Report_on_Virtual_Prototyping_of_Ground_Vehicles

http://www.researchgate.net/publication/265323638_Technical_Report_on_Virtual_Prototyping_of_Ground_Vehicles

http://paws.kettering.edu/~amazzei/student_guide.pdf

http://www.researchgate.net/publication/268351344_Simulation_analysis_and_optimization_design_of_front_suspension_based_on_ADAMS

http://www.researchgate.net/publication/268351344_Simulation_analysis_and_optimization_design_of_front_suspension_based_on_ADAMS

http://link.springer.com/article/10.1007%2FBF02982435

http://www.tandfonline.com/doi/abs/10.1080/00423110801956232

http://www.sciencedirect.com/science/article/pii/S0094114X07000213

https://www.scribd.com/doc/25487188/Using-Adams-PostProcessor-MD-Adams-2010

http://forums.mscsoftware.com/adams/postlist.php?Cat&Board=car

https://simcompanion.mscsoftware.com/infocenter/index?page=home

https://law.resource.org/pub/us/cfr/ibr/005/sae.j1100.2001.html

http://www.fsae.com/forums/forumdisplay.php?45-Open-FSAE-Discussion

http://www.eng-tips.com/viewthread.cfm?qid=389983

http://www.millikenresearch.com/rcvd.html

http://www.f1technical.net/forum/

http://papers.sae.org/800845/

http://www.sae.org/servlets/product%3BWebLogicSession%3FPROD_TYP%3DSTD%26PARENT_BPA_CD%3DGV%26TECH_CD%3DTIRES



http://www.optimumg.com/technical/technical-papers/

https://uwspace.uwaterloo.ca/handle/10012/7824

https://antonaengineering.files.wordpress.com/2012/11/jon_fernandez_de_antona_beng_project_excerpt3.pdf

https://antonaengineering.files.wordpress.com/2012/11/jon_fernandez_de_antona_beng_project_excerpt3.pdf

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